No, this is a different bug than what Belgorad linked. My recommendation would be to reset the quest and try it again, then there's a chance it will work without a bug.
To reset a quest, you need to exit out of the green phase and you may not be on your starship or your stronghold. For example, you can go to Fleet into the public area. Then open the quest window, find the class quest and hit Reset. Then you can do it again from the beginning.
If the quest is still bugged on the second playthrough, you'll have to submit an in-game ticket under the Character/Mission category and include your character name, server name and the name of the quest. Then, Customer Service can manually fix the mission for you but keep in mind that the ticket response time is currently a few weeks, so try fixing it yourself before waiting on Customer Service to fix it.